The newest discoveries are oxygen free because they are so deep and also the hardest to get to. Just ask BP. They panicked when their cap wasn't strong enough but they did have a solution that would (and did work) if not not all that well, it would with modifications and that was to put a tent (funnel) over the leak and let that blow to the surface where they would pump it into a tanker and then skim the oil off the top and filter the sludge and water off the bottom.
Next time they will pore a much heavier cap and be prepared to utilize the technique of separating oil and water in a tanker set up.
I was not clear. None of the process, claimed or otherwise, use oxygen or air to create the hydrocarbon reservoir.
All petroleum deposits are found in sedimentary basins, material laid down from the surface but trapped without a source of oxygen as the sediment builds up.